The catalog can be on any hard drive that is connected to your computer. I have my catalog on the "main" hard drive, and my images are stored on two different internal hard drives as well as an external hard drive. The only time smart previews are used after they have been created is when the master photos are not available to Lightroom. So if you have the master photos on an external hard drive which you disconnect, then the smart previews will be utilized.
Normally you would put the catalog(s) on your internal drive as it is a little faster.
The advantage of placing the catalog on an external drive with the original images is that you can move this drive from computer to computer for ease of sharing.
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Or for the optimum performance have the app locally, the catalog on its own drive and the images on a separate drive allows for the fastest disk access.